Cap/Floor ATM Rate

This is a question on cap volatility market data. The quotes usually include volatilities for different strike (1%, 2%, ... 5%) and maturities (1Y,2Y,...20Y). One volatility for each combination of strike and maturity.

If I want to price a cap with, let's say, a strike of 2% and maturity in 10 years I would use the corresponding volatility from the market data described above. I think I understand it so far.

But then I also have volatility quotes for the at-the-money (ATM) rate. How do I know what the current at-the-money rate is? Second, in which situation would I use the ATM quotes?

• To find the ATM rate you have to look at swaps of the corresponding maturity. – noob2 Nov 8 '17 at 20:55
• Just trying to rephrase your answer to make sure I understand it: When I have a 10y cap and the cap strike is by incident the 10y swap rate, then I would use the ATM-10Y cap volatility for pricing. Is that right? – rokeby Nov 8 '17 at 21:11
• Yes. But it is not a rare event, a considerable amount of business gets done at that rate. – noob2 Nov 8 '17 at 21:21
• And why is that? Why would I want to have a cap with this strike? – rokeby Nov 8 '17 at 22:29

So, let us start with writing the cap / floor parity: $$Cap(K) - Floor(K) = Swap(K)$$ where $$Swap(K)$$ is a swap paying K and that has the exact same characteristics (maturity, schedule, etc.) as the cap and floor.
The ATM level is then the one for which $$Swap(K) = 0$$, and that is, by definition, the swap rate of this swap.